# Definition:General Logarithm/Common

(Redirected from Definition:Common Logarithm)

## Definition

Logarithms base $10$ are often referred to as common logarithms.

## Examples

### Common Logarithm: $\log_{10} 2$

The common logarithm of $2$ is:

$\log_{10} 2 \approx 0.30102 \, 99956 \, 63981 \, 19521 \, 37389 \ldots$

### Common Logarithm: $\log_{10} 3$

The common logarithm of $3$ is:

$\log_{10} 3 = 0.47712 \, 12547 \, 19662 \, 43729 \, 50279 \ldots$

### Common Logarithm: $\log_{10} e$

The common logarithm of Euler's number $e$ is:

$\log_{10} e = 0 \cdotp 43429 \, 44819 \, 03251 \, 82765 \, 11289 \, 18916 \, 60508 \, 22943 \, 97005 \, 803 \ldots$

### Common Logarithm: $\log_{10} \pi$

The common logarithm of $\pi$ is:

$\log_{10} \pi = 0.49714 \, 98726 \, 94133 \, 85435 \, 12683 \ldots$

## Also known as

Common logarithms are sometimes referred to as Briggsian logarithms or Briggs's logarithms, for Henry Briggs.

In elementary textbooks and on most pocket calculators, $\log$ is assumed to mean $\log_{10}$.

This ambiguous notation is not recommended, particularly since $\log$ often means base $e$ in more advanced textbooks.

## Also see

• Results about logarithms can be found here.

## Historical Note

Common logarithms were developed by Henry Briggs, as a direct offshoot of the work of John Napier.

After seeing the tables that Napier published, Briggs consulted Napier, and suggested defining them differently, using base $10$.

In $1617$, Briggs published a set of tables of logarithms of the first $1000$ positive integers.

In $1624$, he published tables of logarithms which included $30 \, 000$ logarithms going up to $14$ decimal places.

Before the advent of cheap means of electronic calculation, common logarithms were widely used as a technique for performing multiplication.